Comminuting apparatuses of the above-described type are known in very different designs. If commercial or industrial waste, such as wood, is to be comminuted to a particular extent with such apparatuses, the consecutive disposal of several comminuting steps or comminuting steps or mechanisms, for example, is known. Moreover, for impeller breakers for example, it is known to combine a comminuting mechanism with a screening device in order to obtain comminuted material of the desired size or consistency. Such conventional comminuting apparatuses have the common disadvantage that, between the comminuting steps or between the comminuting mechanism and the classification apparatus, the comminuted material must pass through paths or overcome distances, which usually is to be brought about by gravitational or centrifugal forces. Particularly with lightweight, moist or greasy comminuted material, this is usually very difficult to carry out and only with the danger of blocking the apparatus and the like. Moreover, with multi-step comminuting apparatuses, the exact coordination of the individual comminuting steps creates problems. Because of the irregular comminution in a comminuting step, this usually leads to a larger dimensioning of the subsequent step. The design and construction costs associated therewith are appreciable, with the result that the production costs are considerable and that such apparatuses therefore are expensive.